Lattice and Peasant Multiplication

Key idea

Alternative multiplication algorithms using grids or halving and doubling.

In depth

Both methods use place value in disguise. Lattice multiplication writes partial products in a grid then sums along diagonals. Russian peasant halves one number and doubles the other, adding doubles where the halved number is odd; it is binary multiplication.

Worked example

13 × 9: 13 (odd, keep 9), 6 → 18, 3 (odd, keep 36), 1 (odd, keep 72). Sum: 9 + 36 + 72 = 117.

Real-world uses

• Multiplying large numbers by a visual grid method in school
• A doubling method used in historical computing

Common mistake

Forgetting to add the row when the halved number is odd.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Arithmetic & Number Sense

• Repeating Decimals – Decimals with a repeating block are rational and convertible to fractions.
• Compound Interest – Interest earned on principal and past interest.
• Inverse Proportion – When one quantity doubles, the other halves.
• Rational Numbers – Numbers expressible as p/q with integers p, q, q≠0.
• Irrational Numbers – Real numbers that cannot be written as a fraction, such as √2 and π.
• Real Numbers – All rational and irrational numbers; the continuous number line.